This invention pertains to integrated circuit (IC) simulations, and more particularly to methods for accurately simulating the behavior of integrated circuits.
Current day integrated circuits often contain millions of electronic elements within a single chip. The internal structures of these electronic elements are in the sub-micron range, and some of these ICs operate at very high frequencies. Consequently, accurate simulations of the IC designs are essential.
Some tools already exist in the computer aided design (CAD) community for digital extraction and simulation of ICs, and these tools are being adapted for high-speed design. However, these tools often incorrectly model the physical effects, and the accuracy of their results is deficient to the point that they cannot be used for practical designs. This is illustrated in FIG. 1, where IC layout information is provided to computer 1 wherein a computer aided design (CAD) simulation software 2 interacts with software 3 that models the behavior of the IC elements specified in the layout, and results of the simulation are outputted. The method executed in the FIG. 1 prior art system is shown in FIG. 2. Tools also exist in the microwave community, and these tools are reasonably accurate because they account for both the first-order and second order effects (e.g., interaction of components that are not physically connected to each other) using Maxwell equation formulations.
Basically, the way these tools tackle the problem is by subdividing a given structure of conductive materials into a mesh of interconnected, elemental, three-dimensional shapes that are small enough to precisely subsume the given structure and to yield accurate calculations relative to their interactions. FIG. 4 illustrates multi-layer arrangement of conducting elements that includes a coil 12 at the lower layer, and a collection of leads 11 at the upper layer. With a subdivision of the structure into a collection of elemental pyramids structures such as shown, for example, in a portion of FIG. 4, a solution is obtained by use of numerical methods and precise mathematical representation of the interaction between each of the elemental three-dimensional shapes and all other of the elemental three-dimensional shapes.
The notion of subdividing the given structure into a mesh of elemental three-dimensional shapes and then performing calculations pertaining to those shapes is not unlike the concept used in teaching the principles of integration by, for example, illustrating that when a two-dimensional figure like a circle is divided into small elemental geometric shapes (e.g., squares), the sum of the areas of the small elemental geometric shapes approximates the area of the circle, and that the approximation improves as the size of the small elemental geometric shapes is reduced.
While in mathematical integration the elemental geometric shape when dealing in three dimensions is a cube (dx, dy, dz) that diminishes to infinitesimal size, in FIG. 5 the small elemental geometric shape is a pyramid that is more than infinitesimal in size, albeit, significantly smaller that than the smallest discernable element in the IC's layout. Also unlike the mathematical approach of integration, the simulation art employs elemental shapes (such as the pyramids of FIG. 4) of different sizes and perhaps even of different shapes, so as to create an accurate representation of the physical structure and yet not use an inordinately large number of pyramids. This is possible to achieve because all dimensions in an integrated circuit layout are discrete. Still, the existing tools are extremely slow, and their memory requirements are excessive.